Problem:
 f(a()) -> b()
 f(a()) -> f(c())
 a() -> d()
 f(d()) -> b()
 f(c()) -> b()
 d() -> c()

Proof:
 Church Rosser Transformation Processor (critical pair closing system, Thm 2.11):
  f(c()) -> b()
  f(d()) -> b()
  d() -> c()
  critical peaks: joinable
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [d] = 7,
    
    [c] = 6,
    
    [b] = 6,
    
    [f](x0) = x0
   orientation:
    f(c()) = 6 >= 6 = b()
    
    f(d()) = 7 >= 6 = b()
    
    d() = 7 >= 6 = c()
   problem:
    f(c()) -> b()
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [c] = 4,
     
     [b] = 0,
     
     [f](x0) = x0 + 1
    orientation:
     f(c()) = 5 >= 0 = b()
    problem:
     
    Qed